Junhui Kim

EXAMPLES AND FUNCTION THEOREMS AROUND AP AND WAP SPACES

We provide some examples around AP and WAP spaces which are connected with higher convergence properties-radiality, semiradiality and pseudoradiality. We also prove a theorem (Theorem 3.2) that (a) any pseudo-open continuous image of an AP-space is an AP-space and (b) any pseudo-open continuous image of an WAP-space is an WAP-space. This answers the question posed by V. V. Tkachuk and I. V. Yaschenko [10].

NEW CARDINAL FUNCTIONS RELATED TO ALMOST CLOSED SETS

In this paper, we strengthen the properties of approximation by points (AP) and weak approximation by points (WAP) considered by A. Pultr and A. Tozzi in 1993 to define -AP and -WAP for an infinite cardinal . We also strengthen the properties of radial and pseudoradial to define -radial and -pseudoradial for an infinite cardinal . These allow us to consider new cardinal functions related to almost closed sets; AP-number, WAP-number, radial number, and pseudoradial number. We study their properties and show the relationships between them. We also provide some examples around -AP and -WAP which are closely connected with -radial and -pseudoradial.

TOPOLOGICAL OPERATIONS OF ITERATED STAR-COVERING PROPERTIES

In this paper, we study topological operations of iter- ated star covering properties, i.e., subspaces, products, and images and preimages of iterated starcompact spaces.

ON STARCOMPACTNESS VERSUS COUNTABLE PRACOMPACTNESS

In this paper, we consider countable version of star cov- ering properties to get interesting results about the relationship between starcompactness and countable pracompactness. We also construct examples related to countable pracompactness and H- closedness.